Marlborough will loan staff, share expertise and provide facilities to the state school.
It coincides with government plans for independent schools to open and manage state schools in deprived areas.
Swindon Academy in Wiltshire is the first "all-through" academy, taking children from infants up to the end of secondary school.
It opened earlier this month, taking over from the struggling Headlands School, which had the worst GCSE results in England two years ago.
The partnership between the two schools will include linking some departments and supporting the establishment of a new sixth form at the academy.
They will share relevant expertise - in areas such as sport or performing arts - to develop joint ventures which would benefit young people in both establishments.
The two schools will also share facilities where it is appropriate and feasible.
